Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.Siirretty Doriast

Supply Chain Optimisation in Animal Husbandry

The pig husbandry is an important economic sector. In the last decade, major changes have been made. As a result, farmers came together to introduce the "Eco Label pig", meeting the strong consumer and governmental call for high quality, animal friendly and environmentally friendly food. The market for Eco Label food is expected to grow enormously in the next years, asking for the development of an efficient and effective supply chain consisting of farmers, slaughter houses, wholesalers and retailers. We present some mathematical models to support decision making and evaluation of a large number of growth scenario's, using cost minimization given a number of Eco Label conditions.supply chain management;logistics;agricultural logistics;network configuration

A bi-objective model for emergency services location-allocation problem with maximum distance constraint

In this paper, a bi-objective mathematical model for emergency services location-allocation problem on a tree network considering maximum distance constraint is presented. The first objective function called centdian is a weighted mean of a minisum and a minimax criterion and the second one is a maximal covering criterion. For the solution of the bi-objective optimization problem, the problem is split in two sub problems: the selection of the best set of locations, and a demand assignment problem to evaluate each selection of locations. We propose a heuristic algorithm to characterize the efficient location point set on the network. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed algorithms

Bottling plant location of microbreweries in East Midlands area, UK

Facility location decisions are critical in real-life projects, which impact on profitability of investment and service levels from demand side. In this paper, a project-based facility location problem should be resolved which refers to the establishment of a centralized bottling plant to serve microbreweries in East Midlands area of UK. This problem will be structured by firstly finding a mathematically theoretical location using the centre-of-gravity method and then formulate the problem as a multi-criteria decision making problem applying Analytical Hierarchy Process based on selection of the optimal location out of the four candidate locations where three of those have been given. The second part is modeled by considering several criteria related to both the activities before and after bottling and also issues of surrounding area of the location where the prioritization of those criteria are based on the preferences of the project investor. The final result is obtained by applying EXPERT CHOICE to approach Eigenvalue methods to enhance Analytical Hierarchy Process. The outcome can be clarified with illustration of the sensitivities resulted from the weight changes of criteria and the pull-out of certain criteria. Key Words: Facility Location, center-of-gravity method, Multi-criteria decision making, Analytical Hierarchy Proces

Facility location optimization model for emergency humanitarian logistics

Since the 1950s, the number of natural and man-made disasters has increased exponentially and the facility location problem has become the preferred approach for dealing with emergency humanitarian logistical problems. To deal with this challenge, an exact algorithm and a heuristic algorithm have been combined as the main approach to solving this problem. Owing to the importance that an exact algorithm holds with regard to enhancing emergency humanitarian logistical facility location problems, this paper aims to conduct a survey on the facility location problems that are related to emergency humanitarian logistics based on both data modeling types and problem types and to examine the pre- and post-disaster situations with respect to facility location, such as the location of distribution centers, warehouses, shelters, debris removal sites and medical centers. The survey will examine the four main problems highlighted in the literature review: deterministic facility location problems, dynamic facility location problems, stochastic facility location problems, and robust facility location problems. For each problem, facility location type, data modeling type, disaster type, decisions, objectives, constraints, and solution methods will be evaluated and real-world applications and case studies will then be presented. Finally, research gaps will be identified and be addressed in further research studies to develop more effective disaster relief operations

Bottling plant location of microbreweries in East Midlands area, UK

Facility location decisions are critical in real-life projects, which impact on profitability of investment and service levels from demand side. In this paper, a project-based facility location problem should be resolved which refers to the establishment of a centralized bottling plant to serve microbreweries in East Midlands area of UK. This problem will be structured by firstly finding a mathematically theoretical location using the centre-of-gravity method and then formulate the problem as a multi-criteria decision making problem applying Analytical Hierarchy Process based on selection of the optimal location out of the four candidate locations where three of those have been given. The second part is modeled by considering several criteria related to both the activities before and after bottling and also issues of surrounding area of the location where the prioritization of those criteria are based on the preferences of the project investor. The final result is obtained by applying EXPERT CHOICE to approach Eigenvalue methods to enhance Analytical Hierarchy Process. The outcome can be clarified with illustration of the sensitivities resulted from the weight changes of criteria and the pull-out of certain criteria. Key Words: Facility Location, center-of-gravity method, Multi-criteria decision making, Analytical Hierarchy Proces

Supply Chain Optimisation in Animal Husbandry

The pig husbandry is an important economic sector. In the last decade, major changes have been made. As a result, farmers came together to introduce the "Eco Label pig", meeting the strong consumer and governmental call for high quality, animal friendly and environmentally friendly food. The market for Eco Label food is expected to grow enormously in the next years, asking for the development of an efficient and effective supply chain consisting of farmers, slaughter houses, wholesalers and retailers. We present some mathematical models to support decision making and evaluation of a large number of growth scenario's, using cost minimization given a number of Eco Label conditions

AN INTEGRATED MULTI-MODEL OPTIMIZATION AND FUZZY AHP FOR SHELTER SITE SELECTION AND EVACUATION PLANNING

Due to an increasing severity of recent disasters, shelter site selection and evacuation planning have become an essential function for the purpose of helping at-risk persons to avoid or recover from the effect of a disaster. Therefore, this study aims to propose an integrated mathematical optimization and fuzzy analytic hierarchy process for shelter site selection and evacuation planning. The mathematical models are formulated under different constraints and model types, in which the objective of each mathematical model is to minimize the total travel distance. The mathematical models are coded and run in optimizer tool for creating plans. Then, Fuzzy Analytic Hierarchy Process is applied to choose the appropriate plan under uncertainty and vagueness of the expert\u27s opinion. A numerical example with a real case study of a Banta municipality in Thailand is given to demonstrate the application of our conceptual model. This study will be great significance in helping decision makers consider placement of emergency shelters and evacuation planning with respect to both qualitative and quantitative measurement. Moreover, our study can be a guide of the methodology to be implemented to other problems as well

Dominating sets for convex functions with some applications

A number of optimization methods require as a rst step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this note we address the problem of constructing dominating sets for problems whose ob jective is a componentwise nondecreasing function of (possibly an in nite number of ) convex functions, and we show how to obtain a convex dominating set in terms of dominating sets of simpler problems. The applicability of the results obtained is illustrated with the statement of new localization results in the elds of Linear Regression and Location.Dirección General de Investigación Científica y Técnic